Modeling
1. Gene pathway design
Lead-sensitive promoter pbrRA functions in the presence of Pb2+. The inhibitory protein PbrR belongs to the MerR family proteins.
1.1 Promoter Pc of different expression intensity (strong, medium and weak) were used to express the inhibitory protein PbrR.
1.2 Lead-sensitive promoter PpbrA was used to express to reporter gene fluorescent protein.
(The modeling process does not take the signal amplification system into account)
2. Mathematical modeling
The functional relationship between fluorescent protein strength and lead concentration is determined by calculating the kinetic equation using the normal differential equation.
Cases:
X is regulated (promoted or repressed) by y,
dx/dt=a+b*y-c*x
x: concentration of x
y: concentration of y
a: natural expression parameters
b: efficiency (+: promotion, -: inhibition) of regulation of y to x
c: natural degradation rate parameters
1. pbrR protein expression rate
dpbrR/dt=a-b*pbrR
2.pbrR monomer aggregated into dipolymers
2spbrR- >pbrR2 k2 is the chemical reaction balance constant
K2=pbrR2/ ;pbrR2=k2*
3. the ability of pbrR dipolymers to combine with Pb2+
pbrR2+pb->pbrR2_pb k3 is the chemical reaction balance constant
4.pbrR repressor protein negatively regulates red fluorescent protein
The effective pbrR inhibitor protein concentration is pbrR dipolymer minus dipolymer combined with Pb2+.
dRfp/dt=
When the above reaction is in a steady state, a functional relationship between fluorescent protein strength and lead concentration is established.
dpbrR/dt=a-b*pbrR=0
K2=pbrR2/; pbrR2=k2
K3=pbrR2_pb/(pbrR2*pb)
dRfp/dt=0
By combining the various kinetic equations, the functional relationship between the intensity of fluorescent protein and the concentration of lead was obtained. The data obtained by experiment and the parameters of the kinetic equation by using fitting method were utilized to establish a mathematical model of fluorescence intensity and lead concentration.
Results of the modeling:
3. Expected Targets
Each parameter of the model was adjusted so that the intensity of fluorescence signal at the safety indicator of lead concentration (at the vertical line, 0.01mg/L) in drinking water rapidly increases to accurately determine whether the concentration of lead in the solution meets safety standards. Components that meet parameter were attempted to use in the course of experiments, then observe whether the results meet the expectations of model.
Division of labor in modeling: the fitting of model parameters and programming was within the scope of my responsibility. The students were in charge of debugging of parameters to ensure that the model achieves the desired goals.
Obtaining the functional relationship between the fluorescence signal strength and the lead concentration by adjusting the parameters of the input model. By clicking “Save plot”, a picture named after the parameter value in the script directory will be output, and the functional relationship between fluorescence intensity and concentration of lead will display.
4. Reference
https://2010.igem.org/Team:Peking/Project/Biosensor
Modeling synthetic gene oscillators Math Biosci. 2012 Mar;236 (1):1-15. doi: 10.1016/j.mbs.2012.01.001. Epub 2012 Jan 18.